Computational Lithography

This is the first book to address the optimization of resolution enhancement techniques in optical lithography. It provides an in-depth discussion of RET tools that use model-based mathematical optimization approaches. The book starts with an introduction of optical lithography systems, electric magnetic field principles, and fundamentals of optimization; it goes on to describe algorithms for the development of optimal optical proximity correction, phaseshifting mask, offaxis illumination approaches, and their combinations. The accompanying mathematical derivations and MATLABreg; software files make it easy for researchers, scientists, engineers, and graduate students and faculty to apply any of the optimization algorithms.

Dr. Xu Ma received a PhD in electrical and computer engineering from the University of Delaware. He is now with the Electrical Engineering and Computer Science Department at the University of California at Berkeley. Dr. Ma's research interests include computational imaging, signal processing and computational lithography. Dr. Gonzalo R. Arce received a PhD degree in electrical engineering from Purdue University. He is the Charles Black Evans Distinguished Professor of Electrical and Computer Engineering at the University of Delaware and holds the Fulbright-Nokia Distinguished Chair in Information and Communications Technologies. Dr. Arce's fields of interest include nonlinear and statistical signal processing, digital printing, and computational imaging. He is a Fellow of the IEEE for his contributions to the theory and applications of nonlinear signal processing.

Preface	p. xi
Acknowledgments	p. xiii
Acronyms	p. xv
Introduction	p. 1
Optical Lithography	p. 1
Optical Lithography and Integrated Circuits	p. 2
Brief History of Optical Lithography Systems	p. 3
Rayleigh's Resolution	p. 5
Resist Processes and Characteristics	p. 7
Techniques in Computational Lithography	p. 10
Optical Proximity Correction	p. 11
Phase-Shifting Masks	p. 11
Off-Axis Illumination	p. 14
Second-Generation RETs	p. 15
Outline	p. 16
Optical Lithography Systems	p. 19
Partially Coherent Imaging Systems	p. 19
Abbe's Model	p. 19
Hopkins Diffraction Model	p. 22
Coherent and Incoherent Imaging Systems	p. 24
Approximation Models	p. 25
Fourier Series Expansion Model	p. 25
Singular Value Decomposition Model	p. 29
Average Coherent Approximation Model	p. 32
Discussion and Comparison	p. 34
Summary	p. 36
Rule-Based Resolution Enhancement Techniques	p. 37
RET Types	p. 37
Rule-Based RETs	p. 37
Model-Based RETs	p. 38
Hybrid RETs	p. 39
Rule-Based OPC	p. 39
Catastrophic OPC	p. 40
One-Dimensional OPC	p. 40
Line-Shortening Reduction OPC	p. 42
Two-Dimensional OPC	p. 43
Rule-Based PSM	p. 44
Dark-Field Application	p. 44
Light-Field Application	p. 45
Rule-Based OAI	p. 46
Summary	p. 47
Fundamentals of Optimization	p. 48
Definition and Classification	p. 48
Definitions in the Optimization Problem	p. 48
Classification of Optimization Problems	p. 49
Unconstrained Optimization	p. 50
Solution of Unconstrained Optimization Problem	p. 50
Unconstrained Optimization Algorithms	p. 52
Summary	p. 57
Computational Lithography with Coherent Illumination	p. 58
Problem Formulation	p. 59
OPC Optimization	p. 62
OPC Design Algorithm	p. 62
Simulations	p. 64
Two-Phase PSM Optimization	p. 65
Two-Phase PSM Design Algorithm	p. 65
Simulations	p. 68
Generalized PSM Optimization	p. 72
Generalized PSM Design Algorithm	p. 72
Simulations	p. 75
Resist Modeling Effects	p. 79
Summary	p. 82
Regularization Framework	p. 83
Discretization Penalty	p. 84
Discretization Penalty for OPC Optimization	p. 84
Discretization Penalty for Two-Phase PSM Optimization	p. 86
Discretization Penalty for Generalized PSM Optimization	p. 87
Complexity Penalty	p. 93
Total Variation Penalty	p. 93
Global Wavelet Penalty	p. 94
Localized Wavelet Penalty	p. 98
Summary	p. 100
Computational Lithography with Partially Coherent Illumination	p. 101
OPC Optimization	p. 102
OPC Design Algorithm Using the Fourier Series Expansion Model	p. 102
Simulations Using the Fourier Series Expansion Model	p. 105
OPC Design Algorithm Using the Average Coherent Approximation Model	p. 107
Simulations Using the Average Coherent Approximation Model	p. 111
Discussion and Comparison	p. 111
PSM Optimization	p. 115
PSM Design Algorithm Using the Singular Value Decomposition Model	p. 116
Discretization Regularization for PSM Design Algorithm	p. 118
Simulations	p. 118
Summary	p. 122
Other RET Optimization Techniques	p. 123
Double-Patterning Method	p. 123
Post-Processing Based on 2D DCT	p. 128
Photoresist Tone Reversing Method	p. 131
Summary	p. 135
Source and Mask Optimization	p. 136
Lithography Preliminaries	p. 137
Topological Constraint	p. 140
Source-Mask Optimization Algorithm	p. 141
Simulations	p. 141
Summary	p. 145
Coherent Thick-Mask Optimization	p. 146
Kirchhoff Boundary Conditions	p. 147
Boundary Layer Model	p. 147
Boundary Layer Model in Coherent Imaging Systems	p. 147
Boundary Layer Model in Partially Coherent Imaging Systems	p. 151
Lithography Preliminaries	p. 153
OPC Optimization	p. 157
Topological Constraint	p. 157
OPC Optimization Algorithm Based on BL Model Under Coherent Illumination	p. 158
Simulations	p. 159
PSM Optimization	p. 162
Topological Constraint	p. 162
PSM Optimization Algorithm Based on BL Model Under Coherent Illumination	p. 165
Simulations	p. 165
Summary	p. 170
Conclusions and New Directions of Computational Lithography	p. 171
Conclusion	p. 171
New Directions of Computational Lithography	p. 173
OPC Optimization for the Next-Generation Lithography Technologies	p. 173
Initialization Approach for the Inverse Lithography Optimization	p. 173
Double Patterning and Double Exposure Methods in Partially Coherent Imaging System	p. 174
OPC and PSM Optimizations for Inverse Lithography Based on Rigorous Mask Models in Partially Coherent Imaging System	p. 174
Simultaneous Source and Mask Optimization for Inverse Lithography Based on Rigorous Mask Models	p. 174
Investigation of Factors Influencing the Complexity of the OPC and PSM Optimization Algorithms	p. 174
Formula Derivation in Chapter 5	p. 175
Manhattan Geometry	p. 181
Formula Derivation in Chapter 6	p. 182
Formula Derivation in Chapter 7	p. 185
Formula Derivation in Chapter 8	p. 189
Formula Derivation in Chapter 9	p. 194
Formula Derivation in Chapter 10	p. 195
Software Guide	p. 199
References	p. 217
Index	p. 223
Table of Contents provided by Ingram. All Rights Reserved.

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